1. EUDET beam telescope Geant 4 simulation of spatial resolution
Daniel Scheirich,
Zdeněk Doležal, Tobias Haas*, Peter Kodyš, Pavel Řezníček
Faculty of Mathematics and Physics
Charles University, Prague
*DESY
EUDET Kick-off meeting, DESY February 2006

2. Motivation and History2
Motivation and History
JRA1 is supposed to deliver beam telescopes for DESY and other beam tests
DESY electron beam suffers from multiple scattering
Geant 4 simulation needed
Existing model developed for DEPFET beam tests
Modification of the model for EUDET telescopes under way
First results will be shown now

3. Outline Program structure Model validation Geometry of the beam test3
Outline
Program structure
Model validation
Geometry of the beam test
Un-scattered particles
Electron beam simulation
Residual plots for 2 different geometries
CERN 180 GeV pion beam simulation
First results for EUDET geometry
Conclusions

4. Geant 4 simulation program
More about Geant 4 framework at
C++ object oriented architecture
Parameters are loaded from files
G4 simulation program
g4run.mac
class
TPrimaryGeneratorAction
g4run.config
class
TGeometry …
class
TDetectorConstruction
class
TDetector …
detGeo1.config
C++ object oriented architecture, using Geant 4 framework
Geometry parameters are loaded from files:
easy way to change a test configuration
no need to re-compile the whole program
Two important classes that loads config files:
TPrimaryGeneratorAction holds an information about particle, energy, energy cuts, …
TDetectorConstruction provides routines to create detector model
ALL geometry parameters loaded from files
Each instance of TGeometry class represents one type of detector (f.i. telescope)
Each instance of TDetector represents one detector in beamtest (f.i. TEL0)
FILE geometry.config: possitions of detectors and sensitive wafers
detGeo2.config …
geometry.config
det. position,
det. geometry files
sensitive wafers

5. 5
Model validation
Simulation of an electron scattering in the 300m silicon wafer
Angular distribution histogram
Comparison with a theoretical shape of the distribution. According to the Particle Physics Review it is approximately Gaussian with a width given by the formula:
Motivation
Scattering in simple wafer – WELL KNOWN PROBLEM
Can be compared
where p,  and z are the momentum, velocity and charge number, and x/X0 is the thickness in radiation length. Accuracy of 0 is 11% or better.

6. Example of an electron scattering6
Example of an electron scattering
Angular distribution
electrons
Electrons move along x-axis
Blue area represents a silicon wafer
Electrons leave wafer in many different directions
Scatter angles are put into histogram
Silicon wafer

7. 7 Non-gaussian tails Gaussian fit Theoretical shape Good agreement
Some numbers will be shown on the next slide
Non-gaussian
tails

8. Results: simulation vs. theory8
Results: simulation vs. theory
0… width of the theoretical
Gaussian distribution
…width of the fitted
Gaussian
accuracy of 0 parametrisation (theory) is 11% or better
According to PPR: accuracy of theta0 is 11% or better
We are safely in the error range
TABLE: Last column is the most interesting
Good agreement between the G4 simulation and the theory

9. Geometry of the DEPFET beam test9
Geometry of the DEPFET beam test
(DEPFET)
Beam is parallel with x-axis
Two and two telescopes, DUT in the center and all is enclosed by scintillators
We will discuss results for different distances b and e
Geometry parameters: Lars Reuen
Electron beam: 3x3 mm2, homogenous, parallel with x-axis

10. Geometry of the beam test: example10
Geometry of the beam test: example
The same thing in VRML

11. Configurations used for the simulation11
Configurations used for the simulation
as planned for January 2006 TB – info from Lars Reuen, October 2005
Geometry 1
Module windows:
50 m copper foils
no foils
150 m copper foils
We have tested 2 geometries:
Telescopes close together – GEOMETRY 1
Telescopes far from each other – GEOMETRY 2
Another tested parameter: window thickness
MOTIVATION:
Use no windows and put the telescopes into one black box
OR use current configuration with separate modules
Geometry 2
Module windows:
50 m copper foils

12. Unscattered particle (geometry only)12
Unscattered particle (geometry only)
Intersects of an unscattered particle lie on a straight line.
A resolution of telescopes is approximately
pitch/(S/N) ~ 2 m.
Positions of intersects in telescopes plane were blurred with a Gaussian to simulate telescope resolution.
These points were fitted by a straight line.
For better understanding of results we will discuss different contribution to the final beam test ressolution.
Non-scattering particle: contribution of telescope intrinsic resolution (resolution of one telescope)
Non-scattering particle = straight line
Every deviations are caused by telescopes’ position errors

13. 13 Residual R(y) in DUT plane
Stars represents intersects of actual track
Black crosses represents errors according to GAUSSIAN distribution, histograms bellow
THOSE BLACK CROSSES are fitted (red line)
We are interested in the residual in the DUT plane

14. Residual distribution in DUT: unscattered particle14
Residual distribution in DUT: unscattered particle
2 cut : width
100% :  = m
70% :  = m
Example of residual plots: geometry 1
Chi square cuts were applies to exclude bad fits
First row is without any chi2 cut
As chi2 cuts are applied width of residual plots in telescopes’ plane decreases while in DUT plane REMAINS THE SAME.
Note that THESE distributions (telescopes) are no longer GAUSSIAN
I will show some numbers -> NEXT SLIDE
50% :  = m
30% :  = m

15. Unscattered particles: residual plots15
Unscattered particles: residual plots
Geometry 1
 = 1.19 m
 = 1.60 m
 = 1.60 m
 = 1.18 m
 = 0.99 m
Geometry 2
SUMMARY for two geometries
ALSO no significant change => we can’t reduce this effect by changing telescopes’ distances
 = 1.05 m
 = 1.68 m
 = 1.68 m
 = 1.05 m
 = 0.99 m

16. Electron beam simulation16
Electron beam simulation
There are 2 main contributions to the residual plots RMS:
Multiple scattering
Telescope resolution
Simulation was done for 1 GeV to 5 GeV electrons, events for each run
Particles that didn’t hit the both scintillators were excluded from the analysis
2 cuts were applied to exclude bad fits
2 contributions to the residual plot width:
Multiple scattering
Detector resolution: beside telescopes there is also DUT resolution that contribute to the final test beam resolution

17. Example of 2 cuts 17 30% of events, 2 < 0.0005
An example of chi2 cut
Colored areas contain 30, 50 or 70% of all events. Chi2 cut corresponds to the right border of an area.
Chi2 is not normalized

18. 18 Actual position DUT residual DUT plane
Telescope resolution: Gaussian with  = 2 m
An example of fitting:
Stars represents intersects of an actual track.
An error according to the Gaussian distribution with a sigma 2 microns is add to the actual intersects in telescope planes.
A residual is distance between fitted straight line and actual position (as is shown in green circle).

19. Electron beam simulation: residual plots19
Electron beam simulation: residual plots
Example of residual plots
Decrease of residual plots width after chi2 cuts were applied IS significant here
And some numbers …

20. Electron beam simulation: residual plots20
Electron beam simulation: residual plots
… and some numbers.
We can reduce DUT residual plot sigma from almost 40 microns to 21 (or less) microns by applying chi2 cuts
BUT there is limit as will be shown further.

21. Residual-plot sigma vs. particle energy21
Energy dependency:
For higher energies multiple scattering runs lower that means narrower residual plots.
For more strict chi2 cuts residual plots are narrower too.
BUT: neither energy nor chi2 cut affect intrinsic DUT and TEL resolution.
That’s why we CAN’T go under ~9 microns

22. Residual plots: two geometries22
Residual plots: two geometries
Ideal detectors
telescopes resolution included
Summary chart [čárt]
RED lines: values of DUT residual plots sigma with ideal detectors
BLACK lines: values of DUT residual plots sigma when all effects are included.
EXPLAIN: cuts and energies
Note:
Significant difference between geometries for less strict cuts & lower energies
For higher energies and more strict cuts difference decrease.

23. Residual plots: two geometries23
Residual plots: two geometries
Ideal detectors
telescopes resolution included
Summary chart [čárt]
RED lines: values of DUT residual plots sigma with ideal detectors
BLACK lines: values of DUT residual plots sigma when all effects are included.
EXPLAIN: cuts and energies
Note:
Significant difference between geometries for less strict cuts & lower energies
For higher energies and more strict cuts difference decrease.

24. Three windows thicknesses for the geometry 124
Three windows thicknesses for the geometry 1
Geometry 1
Module windows:
no foils
50 m copper foils
150 m copper foils
Shortly about window thickness dependency.
Three thicknesses were simulated: 0, 50 & 150.
All for geometry 1.

25. Residual plots: three thicknesses25
Residual plots: three thicknesses
Ideal detectors
TEL & DUT resolution included
We expect: no window is the best.
Let’s see some numbers…

26. Residual plots: three thicknesses26
Residual plots: three thicknesses
Ideal detectors
TEL & DUT resolution included
We expect: no window is the best.
For low energy and less strict cuts it’s true (SHOW)
BUT: for the highest ENG and the most strict cut the values are almost the same, again.
Let’s see some numbers…

27. Pion beam simulation CERN 180 GeV pion beam was simulated27
Pion beam simulation
CERN 180 GeV pion beam was simulated
Geometries 1 and 2 were tested
In addition: the same with pion beam.

28. Pion beam: residual plots28
Pion beam: residual plots
Ideal detectors
TEL & DUT resolution included
Let’s skip to the results: residual plots
Pion has much lower multiple scattering.
Resolution of detectors is much more important.
Note:
For ideal detectors chi2 cut affect residual plot width.
For non-ideal it doesn’t. This effect is washed out by DUT intrinsic resolution.

29. Pion beam: residual plots29
Pion beam: residual plots
Ideal detectors
TEL & DUT resolution included
Numbers confirm it.

30. The latest results Final beam test geometry: similar to the Geometry 1
DUT is shifted to the front side
The resolution of telescopes ~ 5 m

31. Unscattered particle 2 cut : width 100% :  =2.53  0.02 m
Telescope resolution 5 m

32. Infinite energy extrapolation
Telescopes resolution 5 m
Plot 2 vs. 1/E2
Angular distribution width  due to a multiple scattering is proportional to 1/E

33. Infinite purity extrapolation
Attempt to exclude scattered tracks by Chi2 cut – infinite purity

34. Infinite purity and energy extrapolation
Even the most stringent cut cannot eliminate multiple scattering effects

35. 35
EUDET Geometry
The same thing in VRML

36. 6 vs 4 telescopes unscattered particles
6 telescopes give better precision due to more measurement points
6 telescopes 1.0 mm
4 telescopes 1.3 mm

37. 6 vs 4 telescopes scattering included, ideal telescopes
6 telescopes give worse precision due to more scattering
6: mm
4: mm

38. 6 vs 4 telescopes scattering included, telescopes s~2.5 mm
6 telescopes give worse precision due to more scattering: more points won’t overweigh scattering
6: mm
4: mm

39. Distance dependence
Distance matter, so all attempts should be made to get as close as possible

40. 40
Conclusions
Software for a simulation and data analysis has been modified for EUDET
First results available:
4 telescopes better than 6
minimizing distance important
To be done:
Thorough analysis
Magnetic field